Imaging Rainfall Infiltration Processes with the Time-Lapse Electrical Resistivity Imaging

Method

GANG ZHANG,1,2 GUI-BIN ZHANG,1 CHIEN-CHIH CHEN,2 PING-YU CHANG,2 TZU-PIN WANG,2 HORNG-YUAN YEN,2

JIA-JYUN DONG,3 CHUEN-FA NI,3 SU-CHIN CHEN,4 CHAO-WEI CHEN,5 and ZHENG-YUAN JIA1

Abstract—Electrical Resistivity Imaging (ERI) was carried out

continuously for 10 days to map the subsurface resistivity distri-

bution along a potentially hazardous hillslope at the Jieshou Junior

High School in Taoyuan, Taiwan. The reliability of the inverted

resistivity structures down to about 25 m depth was examined with

synthetic modeling using the same electrode arrangements installed

on land surface as in field surveys, together with a DOI (depth-of-

investigation) index calculated from the ERI data. The subsurface

resistivity distribution is consistent with results from well logging.

These ERI recordings were taken daily and provided highly

resolved imagery of the resistivity distribution underground and

illustrated the dynamical fluid-flow behavior due to heavy rainfall

infiltration. Using Archie’s law, the resistivity distribution was

transformed into a map of relative water saturation (RWS), which

is strongly correlated with the rainfall infiltration process. We then

found that the averaged RWS is significantly correlated with daily

precipitation. Our observations indicate that time-lapse ERI is

effective in monitoring subterraneous rainfall infiltration; more-

over, the preferential flow paths can be delineated according to the

changes in averaged RWS derived from the ERI data.

Key words: Electrical resistivity imaging, depth-of-investi-

gation, Archie’s law, rainfall infiltration, preferential path.

1. Introduction

Electrical resistivity imaging (ERI) has been

widely used in resource exploration, hydrogeology

surveys, engineering geology surveys, and environ-

ment geology surveys (AHMED and SULAIMAN 2001;

CHANG et al. 2012; DE BARI et al. 2011; DRAHOR et al.

2011; FIKOS et al. 2012; HERMANS et al. 2012a, b;

LEHMANN et al. 2013; LONG et al. 2006; MAITI et al.

2012; MARTINEZ-PAGAN et al. 2010; METWALY et al.

2013; MUCHINGAMI et al. 2012; PERRONE et al. 2014;

PUJARI et al. 2007; REVIL et al. 2010; SINGH et al.

2010; SIRHAN and HAMIDI 2013; SONKAMBLE 2014;

SPRINGMAN et al. 2013; TANG et al. 2007; TRAVELLETTI

et al. 2012). It can also be used for monitoring the

groundwater flow and river water discharge patterns

(COSCIA et al. 2011, 2012; HAYLEY et al. 2009; SUZUKI

and HIGASHI 2001). In the recent years, the time-lapse

ERI method has been applied to monitor the prefer-

ential flow paths within the rock/soil mass (DRAHOR

et al. 2011; HERMANS et al. 2012b; MAITI et al. 2012;

MUCHINGAMI et al. 2012) and the geological system of

CO2 storage for the real-time purpose (BERGMANN

et al. 2012; CHRISTENSEN et al. 2006; PICOTTI et al.

2013). Compared with other geotechnical and

hydrological methods used for monitoring rainfall

infiltration processes, the time-lapse ERI method can

perform live, high-resolution monitoring of changes

in the physical properties of a subsurface (PERRONE

et al. 2014) in terms of the variation of subsurface

resistivity distribution. Furthermore, ERI is also cost-

effective for surveying large areas, comparing to the

stream gauging by hydrographic station which is

point measurement by several water source wells. It

is different from the ERI method, applied stream

1 School of Geophysics and Information Technology, China

University of Geosciences, Beijing 100083, China. E-mail:

gz.geophysics@outlook.com; gbzhang@cugb.edu.cn;

jzy@cugb.edu.cn2 Department of Earth Sciences and Graduate Institute of

Geophysics, National Central University, Jhongli, Taoyuan 32001,

Taiwan. E-mail: chencc@earth.ncu.edu.tw; pingyuc@gmail.com;

wtbin@uch.edu.tw; yenhy@earth.ncu.edu.tw3 Graduate Institute of Applied Geology, National Central

University, Jhongli, Taoyuan 32001, Taiwan. E-mail:

jjdong@geo.ncu.edu.tw; nichuenfa@geo.ncu.edu.tw4 Department of Soil and Water Conservation, National

Chung Hsing University, Taichung 402, Taiwan. E-mail:

scchen@nchu.edu.tw5 Land Engineering Consultants Co., Ltd., Nankang, Taipei

115, Taiwan. E-mail: vick@safe100.com.tw

Pure Appl. Geophys. 173 (2016), 2227–2239

� 2016 Springer International Publishing

DOI 10.1007/s00024-016-1251-x Pure and Applied Geophysics

gauging in monitoring groundwater flow by hydro-

graphic station is hard to achieve a highly-resolved

imagery of the resistivity distribution subsurface for

surveying large areas, although it can absolutely

provide high-accuracy information of variations in

rainfall infiltration processes for real time.

This study is primarily focused on measuring the

variation of subsurface resistivity distribution to fre-

quently monitor the changes in groundwater flow due

to heavy rainfall infiltration by ERI method. The very

fact of frequently monitoring by ERI method that the

low-resistivity zone can be described and tracked in

each frequency, therefore, the preferential flow paths

can be delineated from the variation of subsurface low-

resistivity zone and the dynamical fluid-flow behavior

due to heavy rainfall infiltration can be illustrated.

Furthermore, by using Archie’s Law, a map of relative

water saturation (RWS) can be produced from ERI

images, in which case the subsurface variations in

rainfall infiltration processes are clearly expressed.

Generally, there are lots of research achievements

about application of ERI in monitoring groundwater

flow due to infiltration of river water (COSCIA et al.

2012) and monitoring the preferential flow paths

within the soil mass (MAITI et al. 2012), imaging arti-

ficial salt water infiltration (HERMANS et al. 2012b), and

so on, however, there are few applications of time-

lapse ERI method in monitoring the rainfall infiltration

for real time at a potentially hazardous hillslope which

is meaningful and valuable. From the time-lapse ERI

method, we can get the high-resolution subsurface

electrical conductivity distribution for real time; then,

the changes of subsurface electrical conductivity grid

block and RWS are monitored for the period of the

rainfall infiltration. Based on the subsurface resistivity,

RWS map obtained from resistivity inversion and the

information from the other data such as drilling data

and rainfall amount from the weather report, the

landslide slippage surface and predominant pathway of

rainfall can be evaluated.

2. Forward Solution and Inversion Strategy for ERI

The equation governing the DC (direct current)

response due to a point current source is given by

(TELFORD et al. 1976; TELFORD and SHERIFF 1990):

r � rr/ð Þ ¼ �Id r� rsð Þ; ð1Þ

where / is the electrical potential [V], I is the source

current [A], d r� rsð Þ is the delta function, r and rsare the location of the observation point and current-

source point [m], respectively, and r is the electrical

conductivity [S/m].

The discretization of the resistivity problem dis-

cussed here is based on a theory described by (DEY

and MORRISON 1979). Using the finite difference

method to the resistivity modeling, the unknown

potential at all of the nodes in the grid is evaluated

using incomplete Cholesky-conjugate gradient

(ICCG) technique to obtain accurate and stable solu-

tions. Since the simulation of the whole space is

restricted to the homogeneous half-space, it is

required that the boundary conditions be specified at

each point. Neumann (no-current) boundary

conditions

o/on

¼ 0 ð2Þ

are assigned at the ground surface, z = 0, whereas

Robin boundary conditions

o/on

þ /rcos h ¼ 0 ð3Þ

are assigned far from the source, where h is the angle

between the radial distance r and the outward normal

n.

For direct current resistivity inversion, the

smoothness-constrained least-squares optimization

method (dEGROOT-HEDLIN and CONSTABLE 1990; ELLIS

and OLDENBURG 1994; MARESCOT and LOKE 2003;

RODI and MACKIE 2001) is frequently used. Here, an

iteratively reweighted version of this method

JTi RdJi þ kiWTRmW

� �Dqi

¼ JTi Rdgi � kiWTRmWqi�1 ð4Þ

was employed for resistivity inversion, where gi is the

data misfit vector describing the difference between

the observed values and calculated potential or

apparent resistivity from the forward solution, Dqi isthe change in the model parameters for the ith itera-

tion, qi�1 is the model-parameters vector for the

previous iteration, J is the Jacobian matrix of partial

derivatives, W is the roughness filter, Rd and Rm are

weighting matrices introduced so that different

2228 G. Zhang et al. Pure Appl. Geophys.

elements of the data misfit and model roughness

vectors are given equal weights in the inversion

process, and ki is the damping factor after the ith

iteration, calculated by

ki ¼ k0�10i ð5Þ

with an initially large value (k0 ¼ 108 in this paper).

The number of forward problems per inversion

iteration is one of most influence factors on the effi-

ciency of inverse problem. In the course of resistivity

inversion, comparing two king of methods on com-

puting the Jacobian (sensitivity) matrix which include

a directly solving J (YORKEY et al. 1987) and a similar

procedure for J multiplying an arbitrary vector

x (MACKIE and MADDEN 1993; RODI 1976), we prefer

employing Rodio’s method. Because Yorkey’s method

is required doing one forward problem for each model

parameter for each inversion iteration on one current

source, and the amount of calculation is great when the

grid mesh density is high, the influence of the mesh

grid density to the inverse of efficiency is enormous;

however, the approach for computing Jx and

JTy (Rodio’s method) requires only one forward

problem for each inversion iteration on one current

source. For the resistivity inversion problem with the

multiple current sources, Rodi’s method is much more

efficient and appropriate for this case in field study.

Based on these principles, rapid 2D inversion algo-

rithms that use conjugate-gradient relaxation techniques

to solve the maximum-likelihood inverse equations

were developed for ERI data using the C# language.

3. Simulation Modeling for Estimating the Depth

of Investigation

Determining a depth of investigation (DOI) is one

of th important problems in geophysical inversion.

According to the field study, the ERI method with the

surface array was used for imaging rainfall infiltration

processes. Therefore, a synthetic resistivity model

with surface array employed for resistivity modeling

and inversion need to be established for synthetic

DOI study. What is more, to figure out the sensitivity

of ERI data to the conductivity blocks in depth when

a surface array is installed in the ERI surveys, a

synthetic resistivity model with a stair-shaped

conductive (10 X m) inclusion inside a resistive

background (100 X m) is built according to the

inverted resistivity maps of the field study for 8 days

(Fig. 5) and mathematical statistics study of the val-

ues of inverted resistivity blocks. This model

(Fig. 1a) consists of 140 resistivity blocks, and the

data space comprises 686 observations of electric

potential difference for various dipole–dipole

arrangements taken in the field survey.

The inverted model (Fig. 1b) bears considerable

likeness to the true resistivity model (Fig. la). The

background value of the inverted model is nearly

100 X m, and the near-surface inhomogeneities

consisting of the stair-shaped resistivity distribution

is well delineated down to 25 m deep.

For thoroughly testifying the conclusion of the

testing, a contrast test adopted the alike method. A

synthetic resistivity model with a stair-shaped con-

ductive (10 X m) inclusion inside a resistive

background (100 X m) is built. This model (Fig. 1d)

consists of 70 resistivity blocks and 686 observations.

The inverted model (Fig. 1e) illustrated that the stair-

shaped resistivity distribution is well delineated and

the depth penetration of inversion with the surface

electrical array is 25 m.

Overall, the DOI of inversion can extend 25 m

when we carry out the surface array in filed study.

The purpose of numerical simulation and inversion

for the synthetic resistivity model with the surface

array is to estimate the DOI of inversion in the case of

electrode arrangements installed in field study, and

the DOI from the simulation modeling is critical for

the following inversion of the ERI field data.

4. Estimating the depth of investigation using field

data

The simulations based on field arrangements, as

discussed in ‘‘Simulation Modeling for Estimating the

Depth of Investigation’’, illustrate that the DOI is

mainly qualitative (CATERINA et al. 2013). However,

there are several tools to evaluate the inverted images

including the model resolution matrix (R), the cumu-

lative sensitivity matrix (S), and the DOI-index.

According to previous research results, (CATERINA et al.

2011, 2013; DECEUSTER et al. 2014), the numerical

Vol. 173, (2016) Imaging Rainfall Infiltration Processes with the Time-Lapse Electrical Resistivity Imaging Method 2229

benchmark shows that indicators based on R and S are

the most appropriate to appraise resistivity maps in

terms of the exactitude of inverted parameters, and the

DOI index providing mainly qualitative information

for the reliability of inverted images. The DOI index is

more appropriate for this case study on depth of

prospecting of inversion with the electrode arrange-

ments installed on land surface, and different electrode

array geometries have different depths of penetration

(OLDENBURG and LI 1999). DOI index is very important

for estimating the reliability of inverse modeling

because it indicates where the inverted image is well

constrained by the data and where it is not. The cal-

culation of DOI index needs to be implemented

stringently. The empirical DOI index method provides

more accurate information from ERI data measured in

field. This method was introduced by (OLDENBURG and

LI 1999) and modified by (MARESCOT et al. 2003).

In general, this method involves two inversions

carried out using reference models with different

initial resistivity values. The resistivity of the first

reference model is obtained from the averaging the

apparent resistivity. The second reference model is

usually set at ten times that of the first one (LOKE

2001). From the modeled resistivity values, the fol-

lowing DOI index is calculated:

R1;2 x; zð Þ ¼ m1 x; zð Þ � m2 x; zð Þm1r � m2r

; ð6Þ

where m1r and m2r are the resistivity of the first and

second reference models, respectively, and m1 x; zð Þand m2 x; zð Þ are the respective model-cell resistivities

obtained from the first and second inversions. The

distribution in the region of DOI indices trends to

zero, where the inversion produces the same cell

resistivity regardless of the reference-model resistiv-

ity. The cell resistivity with zero DOI index is,

therefore, well-constrained by the data and initial

resistivity model implemented for inversion has

negligible impact on inverse modeling. However, in

the region where there is poorly constrained cell-re-

sistivity data, R x; zð Þ will trend to unity due to the factthat inverted resistivity is similar to the initial resis-

tivity. Thus, the model resistivity in regions where

R x; zð Þ is small are considered ‘‘reliable’’, while in

areas of high R x; zð Þ are not. To reduce the effect of

the damping factor and the choice of the two initial

reference models, the DOI index can be normalized

(a) (b) (c)

(d) (e)

(f)

Figure 1The simulated resistivity model with a stair-shaped conductive inclusion inside a resistive background and inverted image. a True resistivity

model, which is used to generate synthetic data where the forward modeling grid has 14 9 10 rectangular nodes, and is 70 m wide and 50 m

deep. The electrode arrangement is a dipole–dipole array with the current and potential electrodes placed on the surface. The resistivities of

the elements are 100 X m (blue cells) and 10 X m (red cells). b Inverted resistivity model. The number of iterations is 20, and the initial value

for the damping factor (k0) is 108. c The root mean square (RMS error) of the inversion is 0.14 % at 20th iteration. d–f The second synthetic

resistivity model, inverted resistivity model, and RMS error which is employed for comparison testing. The forward modeling grid has

14 9 5 rectangular nodes, and is 70 m wide and 25 m deep with the same electrode array and same number of the ERI data for inversion

2230 G. Zhang et al. Pure Appl. Geophys.

with the maximum value Rmax of R x; zð Þ from Eq. (6)

as follows (MARESCOT et al. 2003; ROBERT et al. 2011)

R x; zð Þ ¼ m1 x; zð Þ � m2 x; zð ÞRmax m1r � m2rð Þ ð7Þ

The model for calculating the DOI index uses cells

that extend to the edges of the survey line, and its depth

range is roughly three to five times the median DOI for

the largest array spacing used (LOKE 2001).

Figure 2 shows a 50-m-deep DOI cross-section

for the ERI data. Figure 2a, b represents two inverse

modeling from resistivity inversion using different

reference models with different resistivity value. The

first reference model is obtained from the average of

the apparent resistivity values, *100 X m. Figure 2c

shows the normalized DOI index, calculated after a

second inversion using an initial model with ten times

the resistivity of the first initial model, *1000 X m.

The normalized DOI-index region (Fig. 2c) shows

that the model resistivity, in areas of 20-meter depth

or greater, is reliable when the DOI index is 0.1.

Meanwhile, the model resistivity is reliable at depths

of 25 m or more when the DOI index is 0.2.

According to the synthetic resistivity modeling

with a stair-shaped conductive inclusion inside a

resistive background, the DOI can reach to about

25 m when the length of the survey line is 70 m.

Incorporating the DOI-index cross-section, we can set

the DOI to 25 m for the inversion of our ERI field

data collected at Jieshou Junior High School.

5. Results

ERI surveys were conducted continuously at Jie-

shou Junior High School in Northwestern Taiwan for

10 days from May 17th to May 26th 2014, though the

data on the 20th and 21st were corrupted due to

lightning strikes. The ERI survey line is perpendic-

ular to the landslide scarp line as shown in Fig. 3.

The mass body shown was creeping to the northwest

continuously and a sliding scarp was found across the

Jieshou Junior High School. In order to monitor

rainfall infiltration processes in the subsoil, and

delineate the preferential flow paths and flow veloc-

ities, our dipole–dipole ERI surveys included 686

observations of electric potential difference, taken

daily, with a survey-line length of 70 m and poten-

tial-electrode spacing of 5 m (Fig. 4a). According to

simulated synthetic resistivity modeling and the DOI-

index region calculated from the ERI for May 17th,

the most reasonable depth of inversion was taken as

25 m. Then, the ERI-data inversion was performed.

The ERI inversions show that the ERI method can

produce high-resolution images (Figs. 4b, 5) of the

subterranean resistivity distribution. Some surface

objects are reflected in the ERI images (Fig. 4b), such

as fault fracture and flowerbeds, which are marked in

the first ERI image. Furthermore, the subsurface

resistivity distribution obtained from inversion of

field ERI data is consistent with results from well

logging (Fig. 4b). The thickness of the high-

Figure 2Normalized DOI-index cross-section for 8 days (from 17 May to 26 May, 2014) and the DOI indices of 0.1 and 0.2 are denoted with black

solid lines

Vol. 173, (2016) Imaging Rainfall Infiltration Processes with the Time-Lapse Electrical Resistivity Imaging Method 2231

resistivity layer reaches to 5 m that corresponds to

the backfilling bed according to drilling data of two

boreholes. The low-resistivity layer below the back-

filling bed corresponds to the tuffaceous clastic rock.

Meanwhile, according to the weather report, there

was heavy rain sometime after May 19th (see the

hyetograph of 10 days in Fig. 7), the changes in

electrical characteristics between the maps of May

19th and 22nd are obvious (Fig. 5). It can be inferred

that the low-resistivity zone extended mostly along

the landslide slippage surface (which marked in

Fig. 5) from May 22nd to the 24th; what is more,

there is compresso-crushed zone on the land surface

(see Fig. 3) corresponding to the projection position

of the subsurface landslide slippage surface (between

the distance of 30 m and 40 m along the survey line).

Figure 3Aerial map of Jieshou Junior High School, Taoyuan, Taiwan. The ERI survey line is perpendicular to the landslide fault strike. There are two

boreholes for monitoring the water level. Two regions of fault fracture and two potential electrodes installed in land surface are marked

2232 G. Zhang et al. Pure Appl. Geophys.

(a)

(b)

(c)

Figure 4Inversion of ERI data measured at Jieshou Junior High School. a Electrode arrangements used for field survey and grid mesh implemented for

inversion. b Shown are two DOI-index curves (at 0.1 and 0.2) are marked by solid black lines and drilling data of two boreholes. In the image,

some characteristics of the surface have been marked, including a fault fracture and a flowerbed. c The core samples from the other two local

boreholes (BI-1 and BI-2) and the depth of BI-1 and BI-2 wells is 30 and 70 m, respectively

Vol. 173, (2016) Imaging Rainfall Infiltration Processes with the Time-Lapse Electrical Resistivity Imaging Method 2233

In addition, the inverted resistivity can be trans-

formed to RWS using Archie’s Law (ARCHIE 2013),

as shown in the following Eq. (8):

q ¼ a/�mS�nw qw; ð8Þ

where q is the bulk resistivity of the rock, qw is the

resistivity of the pore water, and for short period of

monitoring time, the resistivity of the pore water

can be approximated to be constant value, / is the

volume fraction porosity, Sw is the fractional water

saturation, a is the proportionality constant, m is

the cementation factor, and n is the saturation

exponent.

The original RWS is derivable from the Archie’s

Law, as shown in the following Eq. (9). RWSk;t1 is the

water saturation of the t2th day relative to the t1th

day for the kth grid block. Sk;t1w , /�m

k;t1, qk;t1w , qk;t1, ak;t1,

mk;t1 and nk;t1 stand for the fractional water satura-

tion, volume fraction porosity, resistivity of the pore

water, bulk resistivity of the rock, proportionality

constant, cementation factor, and saturation exponent

of the kth grid block on the t1th day, respectively.

RWSk;t1 ¼DSk;t1w

Sk;t1w

¼ Sk;t2w � Sk;t1

w

St1w

¼ak;t2/�mk;t2

k;t2 qk;t2w

.qk;t2

� � 1

nk;t2� ak;t1/�mk;t1

k;t1 qk;t1w

.qk;t1

� � 1

nk;t1

ak;t1/�mk;t1

k;t1 qk;t1w

.qk;t1

� � 1

nk;t1

¼ak;t2/�mk;t2

k;t2 qk;t2w

.qk;t2

� � 1

nk;t2

ak;t1/�mk;t1

k;t1 qk;t1w

.qk;t1

� � 1

nk;t1

� 1

ð9Þ

Because ERI was carried out continuously for only

10 days, it can be considered that there is little change

in volume fraction porosity, resistivity of the pore

water, proportionality constant, and cementation factor

in a short period of time. So the properties of the kth

element can be stated as follows:

ak;t2 ¼ ak;t1;

mk;t2 ¼ mk;t1;

/�mk;t2

k;t2 ¼ /�mk;t1

k;t1 ;

qk;t2w ¼ qk;t1

w :

then, the Eq. (9) can be written

Figure 5Inversion of ERI data measured at Jieshou Junior High School for 8 days. The black solid line marked in the resistivity maps from May 22 to

26 representS the slip plane

2234 G. Zhang et al. Pure Appl. Geophys.

RWSk;t1 ¼ qk;t2

qk;t1

� ��1n

�1 ð10Þ

The substituting resistivity maps into RWS by the

Eq. (10). The resulting RWS map provides a more

intuitive reflection of the variation of subsurface

rainfall infiltration and a more accurate estimation of

subterraneous rainfall infiltration processes and flow

velocities, comparing with the ones from the inverted

resistivity images.

However, when the resistivity of the pore water is

sufficiently high that the electric conductivity of the

mineral grains is a substantial contribution to the

electric conductivity of the aquifer, the formulations

of Archie are no longer valid (KIRSCH 2006). Modi-

fied formulations are also required for material with

surface conductivity like clay.

The calculation of the resistivity of clayey mate-

rial is presented by (FROHLICH and PARKE 1989). They

assume that the bulk conductivity of clayey material

r can be explained by parallel connection of surface

conductivity rSurface and conductivity of pore water

rW with volumetric water content H,

r¼ 1

a� rW �Hk þ rSurface ð11Þ

With the Archie’s Law and the expression of

surface conductivity by (RHOADES et al. 1989a, b), we

can get the RWS of the clay layer as described by

Eq. (12) based on similar principles;

RWSk;t1 ¼ rk;t2 � rSurfer

rk;t1 � rSurfe

� �1n

�1 ð12Þ

or, expressed in terms of resistivity

RWSk;t1 ¼1�qk;t2 � rSurfer

1=qk;t1 � rSurfe

� �1n

�1 ð13Þ

For the surveyed area, the clay content of the

backfilling bed is low with a small surface area.

Moreover, the depth of 5 m below in the surveyed

area is consolidated formation (see Fig. 4c).

According to the results from the core analysis data

of the local two boreholes, the main lithology in the

surveyed area is the sedimentary process with the

products of a volcano. Therefore, the influence of

clay content in near-surface can be neglected.

Equation (10), illustrates that uncertainties exist in

the saturation exponent n and the saturation exponent

has the effect in the value of RWS; however, it will

not affect in the variation tendency of RWS during

the 8 days. Moreover, we care about the variation

tendency of RWS for the 8 days but not the value of

RWS in each day. Therefore, the value of RWS needs

only to be calculated with n = 2.0 by the Eq. (10).

The RWS maps (Fig. 6) show a significant cor-

relation with rainfall infiltration. Figure 5 shows

there was little rainfall on May 18th and 19th, and

heavy rainfall after the 19th. The shallow water has

infiltrated on the 23rd and 24th, because the value of

RWS reduced significantly compared to the 22nd.

However, the RWS increased on the 25th for the

near-surface (up to 5 m, shown in red) because of

heavy rainfall on that day. On the 26th, the near-

surface becomes blue because of rapid infiltration of

rainwater. This indicates that the probability of

landslides is very low since the agglomerate rainfall

on the landslide slippage surface was infiltrated

quickly and without sustained hydraulic pressure

throughout the landslide slippage surface.

The daily precipitation is significantly correlated

with the averaged change of the RWS each day, as

shown in Fig. 7. Here, two values of average RWS

are calculated from the RWS images within the

R = 0.1 and R = 0.2 contour intervals, depending on

different DOI indices. The curves show that the daily

hyetograph is very similar to the two curves of the

averaged RWS. Therefore, the rainfall is significantly

correlated with the average RWS, which validates our

use of Archie’s law to produce RWS images from

ERI data to evaluate rainfall infiltration.

Furthermore, Fig. 8 shows variations of the

average RWS at different depths between the 10- to

20-m and the 30- to 40-m distance marks on the

survey line. It is implemented for further delineating

preferential flow paths and slip plane, because there

are two fracture zones between the 10- to 20-m and

the 30- to 40-m distance at land surface (Fig. 4b).

Most of the RWS variation curves in Fig. 8a show

only a slight deviation during the observation period,

except for the one indicating a 2.5-m depth. On the

other hand, the variation curves in Fig. 8b indicate a

downward migration of the RWS peak plume. These

findings suggest that the wetting front moved through

Vol. 173, (2016) Imaging Rainfall Infiltration Processes with the Time-Lapse Electrical Resistivity Imaging Method 2235

a preferential path occurring between the 10- and

20-m mark on the survey line. Thus, the infiltration

took place very rapidly and we are not able to find a

gradually moving wetting plume here. Furthermore,

we are able to estimate the infiltration rate between

30 and 40 m from the migration of the RWS peak

induced by the rain. An infiltration rate of 4 m/day

can be calculated from the slope of the migrating

Figure 6Relative water saturation (RWS) map with the saturation exponents n = 2.0. DS0518�0517=S0517 stands for the water saturation of May 18th

relative to May 17th

Figure 7Hyetograph and average RWS for depths of up to 20 and 25 m, with the DOI index at 0.1 and 0.2, respectively

2236 G. Zhang et al. Pure Appl. Geophys.

RWS-variation peaks in the region. We assert that

this infiltration rate applies to undisturbed soil and

may be much higher through the preferential path

existing between 10 and 20 m.

6. Discussion and Conclusions

ERI was carried out on a hillslope using a dipole–

dipole array with the current and potential electrodes

installed on the land surface, making a valid DOI

necessary for inversion interpreting. There are some

appraisal tools regularly used in inverted images,

such as the model resolution matrix, the cumulative

sensitivity matrix, and the DOI-index. However, the

DOI-index can be used for evaluating the reliability

of inverse modeling, and it is appropriate for the

inversion of field ERI data with electrode arrange-

ments installed on land surface. The two methods

used to evaluate the DOI for inversion were in

agreement: the first simulated resistivity model with a

stair-shaped conductive inclusion inside a resistive

background and predicted a DOI close to about 23 m:

the second method, namely DOI-index sectioning,

indicated that the modeled resistivity was reliable for

a depth of 25 m along a 70-m-long survey line. Then,

based on these previews, an initial resistivity model

with 70 m in distance and 25 m in depth is employed

for inversions of acquired ERI data for 8 days were

performed.

The inversions confirm the viability of ERI in

tracking the movement of groundwater flow and

rainfall infiltration by recording the variation of

subsurface resistivity distribution. Meanwhile, RWS

maps can be obtained from ERI images via Archie’s

Law, which provide a more intuitive reflection of the

variation of subsurface rainfall infiltration, preferen-

tial flow paths, and slip plane. The average RWS,

meanwhile, is calculated from RWS images at depths

of up to 20 and 25 m in our case. After careful study

and comparison, a hyetograph was produced that was

very similar to the two curves of average RWS. From

the hyetograph, the rainfall is significantly correlated

with the average RWS; thus the rainfall infiltration

characteristics evaluated by RWS images is reliable.

Overall, time-lapse ERI method is for the first

time applied to monitor the rainfall infiltration for

real time at a potentially hazardous hillslope. It is

meaningful and valuable for us to provide much more

information about variation of subsurface resistivity

distribution. According to the changes of subsurface

electrical resistivity distribution, we can better

understand the landslide hazard combining with

hydrologic data from the stream gauging. Comparing

to the stream gauging by hydrographic station which

is point measurement by several water source wells,

ERI can obtain the highly resolved imagery of the

resistivity distribution underground. Joint inversion

or investigation of the ERI data from field survey and

hydrologic data from stream gauging in a potentially

hazardous hillslope should be a development trend of

technique for prediction and evaluation of landslide

in the future.

Acknowledgments

This work was co-supported by China Geology

Survey under Grant No. 12120113098800 and Grant

No. 1212011120204. CCC is grateful for research

(a)

(b)

Figure 8Variations of the average RWS at depths between a 10- to 20-m

and b 30- to 40-m distance marks on the survey line

Vol. 173, (2016) Imaging Rainfall Infiltration Processes with the Time-Lapse Electrical Resistivity Imaging Method 2237

support from the Ministry of Science and Technol-

ogy, Taiwan, and the Department of Earth Sciences at

National Central University, Taiwan. The raw data of

the ERI measurements are available from the author

upon request.

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(Received June 15, 2015, revised January 14, 2016, accepted January 29, 2016, Published online February 22, 2016)

Vol. 173, (2016) Imaging Rainfall Infiltration Processes with the Time-Lapse Electrical Resistivity Imaging Method 2239